Model theory of a Hilbert space expanded with an unbounded closed selfadjoint operator

We study a closed unbounded self‐adjoint operator Q acting on a Hilbert space H in the framework of Metric Abstract Elementary Classes (MAECs). We build a suitable MAEC for such a structure, prove it is ?₀‐categorical and ?₀‐stable up to a system of perturbations. We give an explicit continuous axiomatization for the class. We also characterize non‐splitting and show it has the same properties as non‐forking in superstable first order theories. Finally, we characterize equality, orthogonality and domination of (Galois) types in that MAEC.     

On higher-dimensional Courant algebroids

We define the transgression functor which associates with a (higher-dimensional) Courant algebroid on a manifold a Lie algebroid on the shifted tangent bundle of the manifold.     

Crystal and Molecular Structures of Two Triazole Derivatives: 4-Cyclopropyl-4,5-dihydro-1H-1,2,3-triazole and Methyl 1-benzyl-1H-1,2,3-triazole-4-carboxylate

Abstract  

The molecule in 4-cyclopropyl-4,5-dihydro-1H-1,2,3-triazole (I) is disposed about a mirror plane with the triazole ring lying in the plane and being orthogonal to the cyclopropyl ring. Considerable delocalization of π-electron density within the triazole ring is indicated by the pattern of bond distances in (I). The molecule of methyl 1-benzyl-1H-1,2,3-triazole-4-carboxylate (II) adopts a curved shape with the dihedral angle formed between the triazole and benzene rings being 63.23(8)°. By contrast to (I), localization of π-electron density within the triazole ring in (II) is indicated. Both (I), via N–H···N hydrogen bonding, and (II), via C–H···O and C–H···N interactions, associate in the solid state to form supramolecular chains. In (I), the chain is a zigzag with a flat topology, whereas in (II) the linear chain has a curved topology. Compound (I) crystallizes in the orthorhombic space group Pnma with a = 5.6470(2) ?, b = 7.3359(4) ?, c = 13.4404(7) ?, and Z = 4. Compound (II) crystallizes in the monoclinic space group P2₁/c with a = 12.1314(5) ?, b = 5.5951(2) ?, c = 16.4339(7) ?, β = 111.269(2)°, and Z = 4.     

Effect of the Random Defects Generated on the Surface of Pt(111) on the Electro-oxidation of Ethanol: An Electrochemical Study

In the present work, the Pt(111) surface was disordered by controlling the density of {110}- and {100}-type defects. The cyclic voltammogram (CV) of a disordered surface in acid media consists of three contributions within the hydrogen adsorption/desorption region: one from the well-ordered Pt(111) symmetry and the other two transformed from the {111}-symmetry with contributions of {110}- and {100}-type surface defects. The ethanol oxidation reaction (EOR) was studied on these disordered surfaces. Electrochemical studies were performed in 0.1 M HClO₄+0.1 M ethanol using cyclic voltammetry and chronoamperometry. Changes in current densities associated to the specific potentials at which each oxidation peak appears suggest that different surface domains of disordered platinum oxidize ethanol independently. Additionally, as the surface-defect density increases, the EOR is catalysed better. This tendency is directly observed from the CV parameters because the onset and peak potentials are shifted to less positive values and accompanied by increases in the oxidation-peak current on disordered surfaces. Similarly, the CO oxidation striping confirmed this same tendency. Chronoamperometric experiments showed two opposite behaviors at short oxidation times (0.1 s). The EOR was quickly catalyzed on the most disordered surface, Pt(111)-16, and was then rapidly deactivated. These results provide fundamental information on the EOR, which contributes to the atomic-level understanding of real catalysts.     

Development of a Two-velocities Hybrid RANS-LES Model and its Application to a Trailing Edge Flow

The flow around a trailing edge is computed with a new hybrid method designed to more clearly separate the effects of total and sub-grid turbulent stress-modelling on the time-averaged and instantaneous velocity fields, and in turn, mean momentum and kinetic energy balances. These two velocity fields independently define Reynolds averaged and sub-grid-scale viscosities, and distinct stresses, at the same location. In particular, resolved eddies can emerge, or sweep in and out of the Reynolds averaged near wall layer, without being dampened by higher levels of the viscosity in this RANS dominated layer. The two-field hybrid model, first tested on channel flows, gives accurate predictions of mean velocities and stresses for different Reynolds numbers and coarse meshes. For the trailing edge flow the results of the hybrid model are close to the reference fine LES for mean velocity and turbulent content, whereas the DES-SST on the same coarse mesh gives too early separation.     

Microwave-assisted synthesis of 2-aminonicotinic acids by reacting 2-chloronicotinic acid with amines

2-(Methylamino)nicotinic acid was readily prepared in high yield by reacting 2-chloronicotinic acid with 40% aq MeNH₂ under microwave irradiation either at 120 °C for 2 h or at 140 °C for 1.5 h. Subsequently, we found that a range of 2-aminonicotinic acids could be obtained under microwave heating. The optimal reaction conditions involved the use of 3 equiv of amine, water as the solvent and heating at 200 °C for 2 h in the presence of diisopropylethylamine (3 equiv).     

Effect on the aromaticity of heterocyclic ligands by coordination with ruthenium electron-withdrawing metal centers

Density functional theory calculations of polypyridyl ruthenium complexes with polyaromatic ligands have been performed to understand the metal fragment effect on the modulation of their electronic properties and the influence on the aromatic character. The change of positions of the nitrogen atoms in the ligand structure, as well as the metal moiety, seems to influence the electronic behavior of the π-extended structure and the aromatic character of the complexes at both the ground and excited states. In this framework, structural, electronic, and magnetic-based aromaticity indices were used to understand the aromaticity of the free and coordinated ligands. The aromaticity character of the ligands is highly influenced by the metal fragment, and the aromaticity/antiaromaticity is achieved according to both the electron-withdrawing capability of the ligand and the metal fragment. The electronic distribution observed on the aromatic ligand determines their π-stacking ability; thus, it is proposed that the control of the π-stacking ability is modulated according to the electronic nature of the ruthenium moiety.     

Overcoming dissipation in the calculation of standard binding free energies by ligand extraction

This article addresses calculations of the standard free energy of binding from molecular simulations in which a bound ligand is extracted from its binding site by steered molecular dynamics (MD) simulations or equilibrium umbrella sampling (US). Host–guest systems are used as test beds to examine the requirements for obtaining the reversible work of ligand extraction. We find that, for both steered MD and US, marked irreversibilities can occur when the guest molecule crosses an energy barrier and suddenly jumps to a new position, causing dissipation of energy stored in the stretched molecule(s). For flexible molecules, this occurs even when a stiff pulling spring is used, and it is difficult to suppress in calculations where the spring is attached to the molecules by single, fixed attachment points. We, therefore, introduce and test a method, fluctuation‐guided pulling, which adaptively adjusts the spring's attachment points based on the guest's atomic fluctuations relative to the host. This adaptive approach is found to substantially improve the reversibility of both steered MD and US calculations for the present systems. The results are then used to estimate standard binding free energies within a comprehensive framework, termed attach‐pull‐release, which recognizes that the standard free energy of binding must include not only the pulling work itself, but also the work of attaching and then releasing the spring, where the release work includes an accounting of the standard concentration to which the ligand is discharged. © 2013 Wiley Periodicals, Inc.     

Catalytic Activity of Alkali Metal Cations for the Chemical Oxygen Reduction Reaction in a Biphasic Liquid System Probed by Scanning Electrochemical Microscopy

Chemical reduction of dioxygen in organic solvents for the production of reactive oxygen species or the concomitant oxidation of organic substrates can be enhanced by the separation of products and educts in biphasic liquid systems. Here, the coupled electron and ion transfer processes is studied as well as reagent fluxes across the liquid|liquid interface for the chemical reduction of dioxygen by decamethylferrocene (DMFc) in a dichloroethane-based organic electrolyte forming an interface with an aqueous electrolyte containing alkali metal ions. This interface is stabilized at the orifice of a pipette, across which a Galvani potential difference is externally applied and precisely adjusted to enforce the transfer of different alkali metal ions from the aqueous to the organic electrolyte. The oxygen reduction is followed by H₂O₂ detection in the aqueous phase close to the interface by a microelectrode of a scanning electrochemical microscope (SECM). The results prove a strong catalytic effect of hydrated alkali metal ions on the formation rate of H₂O₂, which varies systematically with the acidity of the transferred alkali metal ions in the organic phase.     

The DEPTQ+ Experiment: Leveling the DEPT Signal Intensities and Clean Spectral Editing for Determining CHn Multiplicities

We propose a new ¹³C DEPTQ⁺ NMR experiment, based on the improved DEPTQ experiment, which is designed to unequivocally identify all carbon multiplicities (Cq, CH, CH₂, and CH₃) in two experiments. Compared to this improved DEPTQ experiment, the DEPTQ⁺ is shorter and the different evolution delays are designed as spin echoes, which can be tuned to different ¹J_CH values; this is especially valuable when a large range of ¹J_CH coupling constants is to be expected. These modifications allow (i) a mutual leveling of the DEPT signal intensities, (ii) a reduction in J cross-talk in the Cq/CH spectrum, and (iii) more consistent and cleaner CH₂/CH₃ edited spectra. The new DEPTQ⁺ is expected to be attractive for fast ¹³C analysis of small-to medium sized molecules, especially in high-throughput laboratories. With concentrated samples and/or by exploiting the high sensitivity of cryogenically cooled ¹³C NMR probeheads, the efficacy of such investigations may be improved, as it is possible to unequivocally identify all carbon multiplicities, with only one scan, for each of the two independent DEPTQ⁺ experiments and without loss of quality.